The first component, regulated by \(\lambda _1\) , consists of sparsity-inducing penalties that set unimportant covariate effects to zero, while the second component, regulated by \(\lambda _2\) , consists of fusion penalties that induce parsimony by forcing select parameters to be the same across submodels. Similar penalization frameworks have successfully been used for other models with special structure, including stratified models with coefficients related across strata [1]} and multi-task learning models where a set features is used to simultaneously perform multiple related prediction tasks [2]}.
